Search results for: M-ary Pulse Position Modulation (M-PPM)

Authors: Han-wool Lee, Chin-suk Hong, Weui-bong Jung

Abstract:

In this study, noise characteristics of structure were analyzed in an effort to reduce noise passing through an opening of an enclosure surrounding the structure that generates noise. Enclosures are essential measure to protect noise propagation from operating machinery. Access openings of the enclosures are important path of noise leakage. First, noise characteristics of structure were analyzed and feed-forward noise control was performed using simulation in order to reduce noise passing through the opening of enclosure, which surrounds a structure generating noise. We then implemented a feed-forward controller to actively control the acoustic power through the opening. Finally, we conducted optimization of placement of the reference sensors for several cases of the number of sensors. Good control performances were achieved using the minimum number of microphones arranged an optimal placement.

Keywords: Active Noise Control, Feed-forward Control, Noise Attenuation, Position Optimization.

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Authors: Mary Panko, Rashika Sharma

Abstract:

Sustainability often appears to be an unfamiliar concept to many international students that enrol in a New Zealand technological degree. Lecturers’ experiences with classroom interactions and evaluation of assessments indicate that studying the concept enlightens and enhances international students understanding of sustainability. However, in most cases, even after studying sustainability in their degree programme, students are not given an opportunity to practice and apply this concept into their professions in their home countries. Therefore, using a qualitative approach, the academics conducted research to determine the change in international students understanding of sustainability before and after their enrolment in an Applied Technology degree. The research also aimed to evaluate if international students viewed sustainability of relevance to their professions and whether the students felt that they will be provided with an opportunity to apply their knowledge about sustainability in the industry. The findings of the research are presented in this paper.

Keywords: Education for sustainability, international students, vocational education.

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Authors: Ernst D. Schmitter

Abstract:

Monitoring lightning electromagnetic pulses (sferics) and other terrestrial as well as extraterrestrial transient radiation signals is of considerable interest for practical and theoretical purposes in astro- and geophysics as well as meteorology. Managing a continuous flow of data, automisation of the detection and classification process is important. Features based on a combination of wavelet and statistical methods proved efficient for analysis and characterisation of transients and as input into a radial basis function network that is trained to discriminate transients from pulse like to wave like.

Keywords: transient signals, statistics, wavelets, neural networks

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Authors: Roberto Gaudino, Antonino Nespola, Dario Zeolla, Stefano Straullu, Vittorio Curri, Gabriella Bosco, Roberto Cigliutti, Stefano Capriata, Paolo Solina.

Abstract:

We demonstrate a 40Gbps downstream PON transmission based on PM-QPSK modulation using commercial DFB lasers without optical amplifier in the ODN, obtaining 40dB power budget. We discuss this solution within NG-PON2 architectures.

Keywords: DFB lasers, Optical Coherent Receiver, Passive Optical Networks.

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Authors: Salah I. Al-Mously, Marai M. Abousetta

Abstract:

This paper predicts the effect of the user-s hand-hold position on the Total Isotropic Sensitivity (TIS) of GSM900/1800 mobile phone antennas of realistic in-use conditions, where different semi-realistic mobile phone models, i.e., candy bar and clamshell, as well as different antenna types, i.e., external and internal, are simulated using a FDTD-based platform. A semi-realistic hand model consisting of three tissues and the SAM head are used in simulations. The results show a considerable impact on TIS of the adopted mobile phone models owing to the user-s hand presence at different positions, where a maximum level of TIS is obtained while grasping the upper part of the mobile phone against head. Maximum TIS levels are recorded in talk position for mobile phones with external antenna and maximum differences in TIS levels due to the hand-hold alteration are recorded for clamshell-type phones.

Keywords: FDTD, mobile phone, phantoms, TIS.

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Authors: Paul B. Stone, Subhashini Ganapathy, Mary E. Fendley, Layla Akilan

Abstract:

As notifications become more common through mobile devices, it is important to understand the impact of wearable devices for improved user experience of man-machine interfaces. This study examined the use of a wearable device for a real-time system using a computer simulated petrochemical system. The key research question was to determine how using information provided by the wearable device can improve human performance through measures of situational awareness and decision making. Results indicate that there was a reduction in response time when using the watch and there was no difference in situational awareness. Perception of using the watch was positive, with 83% of users finding value in using the watch and receiving haptic feedback.

Keywords: computer applications, haptic feedback, petrochemical systems, situational awareness, wearable technology

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Authors: Jan Langebach, Peter Fischer, Christian Karcher

Abstract:

A numerical study is presented on convective heat transfer in enclosures. The results are addressed to automotive headlights containing new-age light sources like Light Emitting Diodes (LED). The heat transfer from the heat source (LED) to the enclosure walls is investigated for mixed convection as interaction of the forced convection flow from an inlet and an outlet port and the natural convection at the heat source. Unlike existing studies, inlet and outlet port are thermally coupled and do not serve to remove hot fluid. The input power of the heat source is expressed by the Rayleigh number. The internal position of the heat source, the aspect ratio of the enclosure, and the inclination angle of one wall are varied. The results are given in terms of the global Nusselt number and the enclosure Nusselt number that characterize the heat transfer from the source and from the interior fluid to the enclosure walls, respectively. It is found that the heat transfer from the source to the fluid can be maximized if the source is placed in the main stream from the inlet to the outlet port. In this case, the Reynolds number and heat source position have the major impact on the heat transfer. A disadvantageous position has been found where natural and forced convection compete each other. The overall heat transfer from the source to the wall increases with increasing Reynolds number as well as with increasing aspect ratio and decreasing inclination angle. The heat transfer from the interior fluid to the enclosure wall increases upon decreasing the aspect ratio and increasing the inclination angle. This counteracting behaviour is caused by the variation of the area of the enclosure wall. All mixed convection results are compared to the natural convection limit.

Keywords: Enclosure, heat source, heat transfer, mixed convection.

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Authors: M. Tarafdar Haque, S. Najafi

Abstract:

Improving the reactive power and voltage profile of a distribution substation is investigated in this paper. The purpose is to properly determination of the shunt capacitors on/off status and suitable tap changer (TC) position of a substation transformer. In addition, the limitation of secondary bus voltage, the maximum allowable number of switching operation in a day for on load tap changer and on/off status of capacitors are taken into account. To achieve these goals, an artificial neural network (ANN) is designed to provide preliminary scheduling. Input of ANN is active and reactive powers of transformer and its primary and secondary bus voltages. The output of ANN is capacitors on/off status and TC position. The preliminary schedule is further refined by fuzzy dynamic programming in order to reach the final schedule. The operation of proposed method in Q/V improving is compared with the results obtained by operator operation in a distribution substation.

Keywords: Neuro-fuzzy, Dynamic programming, Reactive power, Voltage profile.

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Authors: Yu-Chen Kuo, Shih-Chieh Lin

Abstract:

Sensor relocation is to repair coverage holes caused by node failures. One way to repair coverage holes is to find redundant nodes to replace faulty nodes. Most researches took a long time to find redundant nodes since they randomly scattered redundant nodes around the sensing field. To record the precise position of sensor nodes, most researches assumed that GPS was installed in sensor nodes. However, high costs and power-consumptions of GPS are heavy burdens for sensor nodes. Thus, we propose a fast sensor relocation algorithm to arrange redundant nodes to form redundant walls without GPS. Redundant walls are constructed in the position where the average distance to each sensor node is the shortest. Redundant walls can guide sensor nodes to find redundant nodes in the minimum time. Simulation results show that our algorithm can find the proper redundant node in the minimum time and reduce the relocation time with low message complexity.

Keywords: Coverage, distributed algorithm, sensor relocation, wireless sensor networks.

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Authors: B. Cynthia Sherin, E. A. Mary Anita

Abstract:

Vehicular Ad-hoc Network (VANET) is an emerging and very promising technology that has great demand on the access capability of the existing wireless technology. VANETs help improve traffic safety and efficiency. Each vehicle can exchange their information to inform the other vehicles about the current status of the traffic flow or a dangerous situation such as an accident. To achieve these, a reliable and efficient Medium Access Control (MAC) protocol with minimal transmission collisions is required. High speed nodes, absence of infrastructure, variations in topology and their QoS requirements makes it difficult for designing a MAC protocol in vehicular networks. There are several MAC protocols proposed for VANETs to ensure that all the vehicles could send safety messages without collisions by reducing the end-to-end delay and packet loss ratio. This paper gives an overview of the several proposed MAC protocols for VANETs along with their benefits and limitations and presents an overall classification based on their characteristics.

Keywords: MAC Protocols, QoS, VANET, V2V, V2I.

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Authors: Rafia Akhter, Aminul Hoque

Abstract:

Solar Cells are destined to supply electric energy beginning from primary resources. It can charge a battery up to 12V dc. For residential use an inverter for 12V dc to 220Vac conversion is desired. For this a static DC-AC converter is necessarily inserted between the solar cells and the distribution network. This paper describes a new P.W.M. strategy for a voltage source inverter. This modulation strategy reduces the energy losses and harmonics in the P.W.M. voltage source inverter. This technique allows the P.W.M. voltage source inverter to become a new feasible solution for solar home application.

Keywords: Boost Inverter, inverter, duty cycle, PWM

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Authors: Yasmin Tantawi, Mary Beth Rosson

Abstract:

In response to the dearth of information about emoji use for different purposes in different settings, this paper investigates the paralinguistic function of emojis within Twitter communication in the United States. To conduct this investigation, the Twitter feeds from 16 population centers spread throughout the United States were collected from the Twitter public API. One hundred tweets were collected from each population center, totaling to 1,600 tweets. Tweets containing emojis were next extracted using the “emot” Python package; these were then analyzed via the IBM Watson API Natural Language Understanding module to identify the topics discussed. A manual content analysis was then conducted to ascertain the paralinguistic and emotional features of the emojis used in these tweets. We present our characterization of emoji usage in Twitter and discuss implications for the design of Twitter and other text-based communication tools.

Keywords: Computer mediated communication, content analysis, paralinguistics, sociology.

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Authors: M. I. Youssef, A. E. Emam, M. Abd Elghany

Abstract:

In this paper, a residue number arithmetic is used in direct sequence spread spectrum system, this system is evaluated and the bit error probability of this system is compared to that of non residue number system. The effect of channel bandwidth, PN sequences, multipath effect and modulation scheme are studied. A Matlab program is developed to measure the signal-to-noise ratio (SNR), and the bit error probability for the various schemes.

Keywords: Spread Spectrum, Direct sequence, Bit errorprobability and Residue number system.

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Authors: J. P. Dubois

Abstract:

Single side band modulation is a widespread technique in communication with significant impact on communication technologies such as DSL modems and ATSC TV. Its widespread utilization is due to its bandwidth and power saving characteristics. In this paper, we present a new scheme for SSB signal generation which is cost efficient and enjoys superior characteristics in terms of frequency stability, selectivity, and robustness to noise. In the process, we develop novel Hilbert transform properties.

Keywords: Crystal filter, frequency drift, frequency mixing, Hilbert transform, phasing, selectivity, single side band AM.

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Authors: J. Grasaesom, S.Thong-om, W. Payakcho, B. Marungsri

Abstract:

This paper presents the experimental results of silicone rubber polymer insulators for 22 kV systems under salt water dip wheel test based on IEC 62217. Straight shed silicone rubber polymer insulators having leakage distance 685 mm were tested continuously 30,000 cycles. One test cycle includes 4 positions, energized, de-energized, salt water dip and deenergized, respectively. For one test cycle, each test specimen remains stationary for about 40 second in each position and takes 8 second for rotate to next position. By visual observation, sever surface erosion was observed on the trunk near the energized end of tested specimen. Puncture was observed on the upper shed near the energized end. In addition, decreasing in hydrophobicity and increasing in hardness were measured on tested specimen comparing with new specimen. Furthermore, chemical analysis by ATR-FTIR was conducted in order to elucidate the chemical change of tested specimens comparing with new specimen.

Keywords: ageing of silicone rubber, salt water dip wheeltest, silicone rubber polymer insulator

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Authors: Li-Chung Su, Chia-Yu Chen, Tzu-Yuan Lai, Sheng-Jye Hwang

Abstract:

Mechanical design of the thin-film solar framed module and mounting system is important to enhance module reliability and to increase areas of applications. The stress induced by different mounting positions played a main role controlling the stability of the whole mechanical structure. From the finite element method, under the pressure from the back of module, the stress at Lc (center point of the Long frame) increased and the stresses at Center, Corner and Sc (center point of the Short frame) decreased while the mounting position was away from the center of the module. In addition, not only the stress of the glass but also the stress of the frame decreased. Accordingly it was safer to mount in the position away from the center of the module. The emphasis of designing frame system of the module was on the upper support of the Short frame. Strength of the overall structure and design of the corner were also important due to the complexity of the stress in the Long frame.

Keywords: Finite element method, Framed module, Mountingposition

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Authors: Rabinder Singh Bharj, Sandeep Kumar

Abstract:

This investigation presents preparation of sample and  analysis of results of ballistic impact test as per EN 1063 on the size,  thickness, number, position, and type of the bonding interlayer  Polyvinyl Butyral, Poly Carbonate and Poly Urethane on bullet proof  glass. It was observed that impact energy absorbed by bullet proof  glass increases with the increase of the total thickness from 33mm to  42mm to 51mm for all the three samples respectively. Absorption  impact energy is greater for samples with more number of bonding  interlayers than with the number of glass layers for uniform increase  in total sample thickness. There is no effect on the absorption impact  energy with the change in position of the bonding interlayer. 

Keywords: Absorbed energy, bullet proof glass, laminated glass, safety glass.

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Authors: Azali Saudi, Jumat Sulaiman

Abstract:

Harmonic functions are solutions to Laplace’s equation that are known to have an advantage as a global approach in providing the potential values for autonomous vehicle navigation. However, the computation for obtaining harmonic functions is often too slow particularly when it involves very large environment. This paper presents a two-stage iterative method namely Modified Arithmetic Mean (MAM) method for solving 2D Laplace’s equation. Once the harmonic functions are obtained, the standard Gradient Descent Search (GDS) is performed for path finding of an autonomous vehicle from arbitrary initial position to the specified goal position. Details of the MAM method are discussed. Several simulations of vehicle navigation with path planning in a static known indoor environment were conducted to verify the efficiency of the MAM method. The generated paths obtained from the simulations are presented. The performance of the MAM method in computing harmonic functions in 2D environment to solve path planning problem for an autonomous vehicle navigation is also provided.

Keywords: Modified Arithmetic Mean method, Harmonic functions, Laplace’s equation, path planning.

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Authors: M. Khajezadeh, M. Saied Fallah Niasar, S. Ali Asli, D. Davani Davari, M. Godarzi, Y. Asgari

Abstract:

This study aims to explore the joint application of both Boston and Ansoff matrices in the operational development of the product. We conduct deep analysis, by utilizing the Artificial Neural Network, to predict the position of the product in the market while the company is interested in increasing its share. The data are gathered from two industries, called hygiene and detergent. In doing so, the effort is being made by investigating the behavior of top player companies and, recommend strategic orientations. In conclusion, this combination analysis is appropriate for operational development; as well, it plays an important role in providing the position of the product in the market for both hygiene and detergent industries. More importantly, it will elaborate on the company’s strategies to increase its market share related to a combination of the Boston Consulting Group (BCG) Matrix and Ansoff Matrix.

Keywords: Artificial neural network, portfolio analysis, BCG matrix, Ansoff matrix.

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Authors: Zuzana Dideková, Beata Mikovičová

Abstract:

Characterization of radio communication signals aims at automatic recognition of different characteristics of radio signals in order to detect their modulation type, the central frequency, and the level. Our purpose is to apply techniques used in image processing in order to extract pertinent characteristics. To the single analysis, we add several rules for checking the consistency of hypotheses using fuzzy logic. This allows taking into account ambiguity and uncertainty that may remain after the extraction of individual characteristics. The aim is to improve the process of radio communications characterization.

Keywords: fuzzy classification, fuzzy inference system, radio communication signals, telecommunications

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Authors: B. Käfer, V. K. Bheemineni, H. Lammer, M. Kotnik, F. O. Riemelmoser

Abstract:

Axial compression tests are performed on circular tubes made of Aluminum EN AW 6060 (AlMgSi0.5 alloy) in T66 state. All the received tubes have the uniform outer diameter of 40mm and thickness of 1.5mm. Two different lengths 100mm and 200mm are used in the analysis. After performing compression tests on the uniform tube, important crashworthy parameters like peak force, average force, crush efficiency and energy absorption are measured. The present paper has given importance to increase the percentage of crush efficiency without decreasing the value energy absorption of a tube, so a circumferential notch was introduced on the top section of the tube. The effects of position and cut-out lengths of a circumferential notch on the crush efficiency are well explained with relative deformation modes and force-displacement curves. The numerical simulations were carried on the software tool ANSYS/LS-DYNA. It is seen that the numerical results are reasonably good in agreement with the experimental results. 

Keywords: Crash box, Notch triggering, Energy absorption, FEM simulation.

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Authors: Vicky Min-How Lim, Siew Fan Wong, Tong Ming Lim

Abstract:

Automatic keyphrase extraction is useful in efficiently locating specific documents in online databases. While several techniques have been introduced over the years, improvement on accuracy rate is minimal. This research examines attribute scores for author-supplied keyphrases to better understand how the scores affect the accuracy rate of automatic keyphrase extraction. Five attributes are chosen for examination: Term Frequency, First Occurrence, Last Occurrence, Phrase Position in Sentences, and Term Cohesion Degree. The results show that First Occurrence is the most reliable attribute. Term Frequency, Last Occurrence and Term Cohesion Degree display a wide range of variation but are still usable with suggested tweaks. Only Phrase Position in Sentences shows a totally unpredictable pattern. The results imply that the commonly used ranking approach which directly extracts top ranked potential phrases from candidate keyphrase list as the keyphrases may not be reliable.

Keywords: Accuracy, Attribute Score, Author-supplied keyphrases, Automatic keyphrase extraction.

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Authors: P. Ramana , K. Alice Mary, M. Surya Kalavathi, M. Phani Kumar

Abstract:

This paper discusses two observers, which are used for the estimation of parameters of PMSM. Former one, reduced order observer, which is used to estimate the inaccessible parameters of PMSM. Later one, full order observer, which is used to estimate all the parameters of PMSM even though some of the parameters are directly available for measurement, so as to meet with the insensitivity to the parameter variation. However, the state space model contains some nonlinear terms i.e. the product of different state variables. The asymptotic state observer, which approximately reconstructs the state vector for linear systems without uncertainties, was presented by Luenberger. In this work, a modified form of such an observer is used by including a non-linear term involving the speed. So, both the observers are designed in the framework of nonlinear control; their stability and rate of convergence is discussed.

Keywords: Permanent magnet synchronous motor, Mathematicalmodelling, Rotor reference frame, parameter estimation, Luenbergerobserver, reduced order observer, full order observer

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Authors: Aini Hussain, M A Hannan, Azah Mohamed, Hilmi Sanusi, Burhanuddin Yeop Majlis

Abstract:

Airbag deployment has been known to be responsible for huge death, incidental injuries and broken bones due to low crash severity and wrong deployment decisions. Therefore, the authorities and industries have been looking for more innovative and intelligent products to be realized for future enhancements in the vehicle safety systems (VSSs). Although the VSSs technologies have advanced considerably, they still face challenges such as how to avoid unnecessary and untimely airbag deployments that can be hazardous and fatal. Currently, most of the existing airbag systems deploy without regard to occupant size and position. As such, this paper will focus on the occupant and crash sensing performances due to frontal collisions for the new breed of so called smart airbag systems. It intends to provide a thorough discussion relating to the occupancy detection, occupant size classification, occupant off-position detection to determine safe distance zone for airbag deployment, crash-severity analysis and airbag decision algorithms via a computer modeling. The proposed system model consists of three main modules namely, occupant sensing, crash severity analysis and decision fusion. The occupant sensing system module utilizes the weight sensor to determine occupancy, classify the occupant size, and determine occupant off-position condition to compute safe distance for airbag deployment. The crash severity analysis module is used to generate relevant information pertinent to airbag deployment decision. Outputs from these two modules are fused to the decision module for correct and efficient airbag deployment action. Computer modeling work is carried out using Simulink, Stateflow, SimMechanics and Virtual Reality toolboxes.

Keywords: Crash severity analysis, occupant size classification, smart airbag, vehicle safety system.

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Authors: Kar Foo Chong, Andreas Lee Astuti, Pradeep K. Gopalakrishnan, T. Hui Teo

Abstract:

This paper describes design of a digital feedback loop for a low switching frequency dc-dc switching converters. Low switching frequencies were selected in this design. A look up table for the digital PID (proportional integrator differentiator) compensator was implemented using Altera Stratix II with built-in ADC (analog-to-digital converter) to achieve this hardware realization. Design guidelines are given for the PID compensator, high frequency DPWM (digital pulse width modulator) and moving average filter.

Keywords: dc-dc converter, FPGA, PID, power management, .

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Authors: Seung You Na, Joo Hyun Jung, Jin Young Kim, Mohammad AhangarKiasari

Abstract:

There are various kinds of medical equipment which requires relatively accurate positional adjustments for successful treatment. However, patients tend to move without notice during a certain span of operations. Therefore, it is common practice that accompanying operators adjust the focus of the equipment. In this paper, tracking controllers for medical equipment are suggested to replace the operators. The tracking controllers use AHRS sensor information to recognize the movements of patients. Sensor fusion is applied to reducing the error magnitudes through linear Kalman filters. The image processing of optical markers is included to adjust the accumulation errors of gyroscope sensor data especially for yaw angles. The tracking controller reduces the positional errors between the current focus of a device and the target position on the body of a patient. Since the sensing frequencies of AHRS sensors are very high compared to the physical movements, the control performance is satisfactory. The typical applications are, for example, ESWT or rTMS, which have the error ranges of a few centimeters.

Keywords: AHRS, Sensor fusion, Tracking control, Position and posture.

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Authors: Pil Woo Heo, In Sub Park

Abstract:

Flows in a microchannel are laminar, which means that mixing depends on only inter-diffusion. A micromixer plays an important role in obtaining fast diagnosis results in the fields of m-TAS (total analysis system), Bio-MEMS and LOC (lab-on-a-chip).

In this paper, we propose a new active mixer with vertical flow placement via a series of inlets for micromixing. This has two inlets on the same axis, one of which is located before the other. The sample input by the first inlet flows into the down-position, while the other sample by the second inlet flows into the up-position. In the experiment, the samples were located vertically in up-down positions in a micro chamber. PZT was attached below a chamber, and ultrasonic waves were radiated in the down to up direction towards the samples in the micro chamber in order to accelerate the mixing. The mixing process was measured by the change of color in a micro chamber using phenolphthalein and NaOH. The results of the experiment showed that the samples in the microchamber were efficiently mixed and that our new active mixer was superior to the horizontal type of active mixers in view of the grey levels and the standard deviation.

Keywords: Active mixer, vertical flow placement, microchannel, bio-MEMS, LOC.

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Authors: Ameni Mokni, Hatem Mhiri, Georges Le Palec, Philippe Bournot

Abstract:

Numerical study of a plane jet occurring in a vertical heated channel is carried out. The aim is to explore the influence of the forced flow, issued from a flat nozzle located in the entry section of a channel, on the up-going fluid along the channel walls. The Reynolds number based on the nozzle width and the jet velocity ranges between 3 103 and 2.104; whereas, the Grashof number based on the channel length and the wall temperature difference is 2.57 1010. Computations are established for a symmetrically heated channel and various nozzle positions. The system of governing equations is solved with a finite volumes method. The obtained results show that the jet-wall interactions activate the heat transfer, the position variation modifies the heat transfer especially for low Reynolds numbers: the heat transfer is enhanced for the adjacent wall; however it is decreased for the opposite one. The numerical velocity and temperature fields are post-processed to compute the quantities of engineering interest such as the induced mass flow rate, and the Nusselt number along the plates.

Keywords: Channel, Heat flux, Jet, Mixed convection.

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Authors: Ernst D. Schmitter

Abstract:

Monitoring lightning electromagnetic pulses (sferics) and other terrestrial as well as extraterrestrial transient radiation signals is of considerable interest for practical and theoretical purposes in astro- and geophysics as well as meteorology. Managing a continuous flow of data, automation of the analysis and classification process is important. Features based on a combination of wavelet and statistical methods proved efficient for this task and serve as input into a radial basis function network that is trained to discriminate transient shapes from pulse like to wave like. We concentrate on signals in the Very Low Frequency (VLF, 3 -30 kHz) range in this paper, but the developed methods are independent of this specific choice.

Keywords: Transient signals, statistics, wavelets, neural networks

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Authors: Alexander B. Bichkov, Valery V. Smirnov

Abstract:

Total cross section of helium atom photo-ionization by weak short pulse is calculated using the variant of trajectory method, developed in our earlier work. The method enables simple estimation of total ionization probability (or cross section) without integration of differential one.

Keywords: Evaluation of Photo-Ionization, Helium, Trajectory Method

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